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FNO and DeepONet are by far the most popular neural operator learningalgorithms. FNO seems to enjoy an edge in popularity due to its ease of use,especially with high dimensional data. However, a lesser-acknowledged featureof DeepONet is its modularity. This feature allows the user the flexibility ofchoosing the kind of neural network to be used in the trunk and/or branch ofthe DeepONet. This is beneficial because it has been shown many times thatdifferent types of problems require different kinds of network architecturesfor effective learning. In this work, we will take advantage of this feature bycarefully designing a more efficient neural operator based on the DeepONetarchitecture. We introduce U-Net enhanced DeepONet (U-DeepONet) for learningthe solution operator of highly complex CO2-water two-phase flow inheterogeneous porous media. The U-DeepONet is more accurate in predicting gassaturation and pressure buildup than the state-of-the-art U-Net based FourierNeural Operator (U-FNO) and the Fourier-enhanced Multiple-Input Operator(Fourier-MIONet) trained on the same dataset. In addition, the proposedU-DeepONet is significantly more efficient in training times than both theU-FNO (more than 18 times faster) and the Fourier-MIONet (more than 5 timesfaster), while consuming less computational resources. We also show that theU-DeepONet is more data efficient and better at generalization than both theU-FNO and the Fourier-MIONet.

U-DeepONet: U-Net Enhanced Deep Operator Network for Geologic Carbon Sequestration